Let a= i+ j- k and c=2 i-3 j+2 k.

Question

Let $\vec a=\hat i+\hat j-\hat k$ and $\vec c=2\hat i-3\hat j+2\hat k$. The number of vectors $\vec b$ with $\vec b	imes\vec c=\vec a$ (magnitudes in $\{1,\dots,10\}$) is:

Accepted Answer

For $\vec b\times\vec c=\vec a$ to have any solution, $\vec a$ must be perpendicular to $\vec c$ (since $\vec b\times\vec c\perp\vec c$ always). But
$$\vec a\cdot\vec c = 2-3-2=-3\ne0$$

So no such $\vec b$ exists.

Solutions · 1